Single-snapshot-based dynamical mode prediction of a flickering flame via a Fourier-neural-operator network

Abstract

The self-excited flickering of jet diffusion flames is dominated by the dynamics of periodic coherent vortical structures, which can typically be analyzed through dynamic mode decomposition (DMD) based on a time-resolved flow-field sequence. We present a neural network that extracts these structures and their energy content instantaneously from a single snapshot of the vorticity field, by leveraging a Fourier neural operator (FNO) combined with a DMD-based output layer that enforces physical interpretability. Trained on direct numerical simulation (DNS) data of different jet flames, the network predication shows good agreement with the classical DMD in capturing the wavelength and pattern of the coherent structures for the three leading instantaneous DMD modes. In reconstructing the vorticity field, the prediction exhibits only about 2% normalized error compared with the original DNS data, preserving the vortex-core trajectory and intensity with normalized errors of approximately 2% and 7%, respectively. These demonstrate the proposed network to be an effective yet lightweight surrogate for dynamic modal analysis of unsteady flames, especially in applications where the system is observable only at limited times.